document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=901220>Question 901220</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of two numbers is 23. If the product of the two numbers must be greater than 76, what pairs of numbers satisfy the conditions if both numbers are integers?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #546574 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=546574\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x and y. They are INTEGERS.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=23 ALIGN=MIDDLE  ALT=\"x%2By=23\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy%3E76 ALIGN=MIDDLE  ALT=\"xy%3E76\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=23-x ALIGN=MIDDLE  ALT=\"y=23-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >; substitute into the inequality.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2823-x%29%3E76 ALIGN=MIDDLE  ALT=\"x%2823-x%29%3E76\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2%2B23x%3E76 ALIGN=MIDDLE  ALT=\"-x%5E2%2B23x%3E76\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2%2B23x-76%3E0 ALIGN=MIDDLE  ALT=\"-x%5E2%2B23x-76%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x%5E2-23x%2B76%3C0%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x%5E2-23x%2B76%3C0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-19%29%28x-4%29%3C0 ALIGN=MIDDLE  ALT=\"%28x-19%29%28x-4%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You want integers between 4 and 19.  You do not want these two values included,<BR>\n" );
document.write( "because the problem specified a strict inequality, product GREATER than 76.<BR>\n" );
document.write( "5 & 18 ? Yes.<BR>\n" );
document.write( "6 & 17 ? Yes.<BR>\n" );
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document.write( "11&12?  Yes.\r<BR>\n" );
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document.write( "ANSWER:  Lowest number 5; highest number 18,<BR>\n" );
document.write( "whose sum is 23.<BR>\n" );
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